The closest I would line breed is 3rd gen - but there are some lines I will not line breed, even if 3d gen. For example, I would not linebreed Sandro Hit, but I would linebreed Loretta, his dam. I would only linebreed Donnerhall if I were fairly confident the particular pairing would not produce too heavy. I would not linebreed Contango, because he is sickle-hocked and I would be afraid that would come through (though leg traits are only 20% heritable). So, first I have the general rule "no closer than 3rd" and then I consider whether linebreeding the particular lines is desirable.
If you could be more specific about the actual bloodlines, I am sure people would have plenty of suggestions.
No, I'd never line breed a Sandro Hit. One good dose is enough. lol
Changing subjects and this may be a different thread.. When you said legs are only 20% heritable. How is that known? I'm interested in knowing what % the other parts are.
What about Caprimond?
The Hanoverian Verband did a study (actually, I believe it was Dr. Ludwig Christmann's study) a while back regarding the heritability of various traits and it culminated in a report with all kinds of interesting statistics. I have a copy of it on my computer that died a sad death due to an ewarmbloods.net virus but if I can locate another copy I will post a link.
RE Caprimond - I would linebreed that in a heartbeat. Caprimond passes on excellent rideability, usually, as well as typiness and good movement. I have a Hohenstein mare with a 10 temperament; she rocks. I have seen some small Caprimonds; on the other hand, some such as Contucci are tall and consistently produce tall.
Edited to add:
Here is a link to a reprint of the Christmann article on heritability referenced above:
I have an acquaintance who bred her Flemmingh son (out of old/tb mare) to her Flemmingh daughter (trak/old/tb). I was informed that Flemmingh should be 3 generation separation. Should be interesting next year to see the product. Some people just don't care, they have the stallion so bred it, even if it's only 2. Each to their own. I believe stallions should be well mannered and started under saddle with a job before being in the breeding shed, except for a few test breds.
it's not the edge of the earth, but you can see it from here
Obviously your question is more specific toward lines.
Two of my mentors, in very different breeds and from very different backgrounds, but both at the top of their games, both agree(d) that Granddaughter to Grandfather or Grandson to Grandmother is one of the most successful ways of solidifying traits. (good or bad, of course, but the aim being GOOD.)
Super interesting articles above, I have bookmarked for when I have more time to 'read for understanding.'